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Chapter 7: Problem 9

Hess's law is really just another statement of the first law of thermodynamics. Explain.

Short Answer

Expert verified
Hess's law and the first law of thermodynamics both focus on conservation principles, with Hess's law conserving enthalpy and the first law conserving energy. Enthalpy is related to internal energy, pressure, and volume, and under constant pressure conditions, the change in enthalpy represents the heat exchanged. Therefore, Hess's law is essentially stating that the total heat exchange in a reaction is constant, which aligns with the first law of thermodynamics' focus on energy conservation, making Hess's law another statement of the first law of thermodynamics.

Step by step solution

01

Understand the First Law of Thermodynamics

The first law of thermodynamics states that energy cannot be created or destroyed, but can only change from one form to another. In other words, the total energy of an isolated system is conserved. Mathematically, it can be expressed as: \(\Delta E = q + w\), where \(\Delta E\) is the change in internal energy, \(q\) is the heat exchanged, and \(w\) is the work done on/by the system.
02

Understand Hess's Law

Hess's law states that the enthalpy change for a given reaction is the same, regardless of the particular way the reaction is carried out. In other words, if a reaction can be expressed as a series of steps, the sum of the enthalpy changes for each step is equal to the enthalpy change for the overall reaction. This is true as long as the initial and final conditions are the same.
03

Compare the Principles of the First Law of Thermodynamics and Hess's Law

Both the first law of thermodynamics and Hess's law are based on the conservation of a certain property of a system. In the case of thermodynamics, it's the conservation of energy, whereas for Hess's law, it's the conservation of enthalpy. These two quantities, though not the same, both relate to the energy changes within a system.
04

Relate Enthalpy to Heat and Internal Energy

Enthalpy (\(H\)) is a state function that represents the total energy of a system. It is related to the internal energy (\(U\)), pressure (\(P\)), and volume (\(V\)) as follows: \(H = U + PV\). For an isobaric (constant pressure) process, the change in enthalpy is equal to the heat exchanged: \(\Delta H = q_p\). This links the concept of enthalpy to the heat term in the first law of thermodynamics equation.
05

Show that Hess's Law is a Reflection of the First Law of Thermodynamics

Since the enthalpy changes in a chemical reaction are equivalent to the heat exchanged in a constant pressure process, Hess's law is essentially stating that the sum of heat exchanges in a series of reactions is equal to the heat exchange in the overall reaction. This aligns with the first law of thermodynamics, which focuses on the conservation of energy in a system, including heat exchanges. Therefore, Hess's law can be considered another statement of the first law of thermodynamics.

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Most popular questions from this chapter

Consider the following reaction: $$\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) \quad \Delta H=-891 \mathrm{kJ}$$ Calculate the enthalpy change for each of the following cases: a. \(1.00 \mathrm{g}\) methane is burned in excess oxygen. b. \(1.00 \times 10^{3} \mathrm{L}\) methane gas at \(740 .\) torr and \(25^{\circ} \mathrm{C}\) are burned in excess oxygen. The density of \(\mathrm{CH}_{4}(g)\) at these conditions is \(0.639 \mathrm{g} / \mathrm{L}\).

Consider 2.00 moles of an ideal gas that are taken from state \(A\) \(\left(P_{A}=2.00 \mathrm{atm}, V_{A}=10.0 \mathrm{L}\right)\) to state \(B\left(P_{B}=1.00 \mathrm{atm}, V_{B}=\right.\) \(30.0 \mathrm{L})\) by two different pathways: These pathways are summarized on the following graph of \(P\) versus \(V:\) Calculate the work (in units of J) associated with the two pathways. Is work a state function? Explain.

Consider the following statements: "Heat is a form of energy, and energy is conserved. The heat lost by a system must be equal to the amount of heat gained by the surroundings. Therefore, heat is conserved." Indicate everything you think is correct in these statements. Indicate everything you think is incorrect. Correct the incorrect statements and explain.

Given the following data $$\begin{array}{cl}\mathrm{P}_{4}(s)+6 \mathrm{Cl}_{2}(g) \longrightarrow 4 \mathrm{PCl}_{3}(g) & \Delta H=-1225.6 \mathrm{kJ} \\ \mathrm{P}_{4}(s)+5 \mathrm{O}_{2}(g) \longrightarrow \mathrm{P}_{4} \mathrm{O}_{10}(s) & \Delta H=-2967.3 \mathrm{kJ} \\\ \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{PCl}_{5}(g) & \Delta H=-84.2 \mathrm{kJ} \\ \mathrm{PCl}_{3}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{Cl}_{3} \mathrm{PO}(g) & \Delta H=-285.7 \mathrm{kJ} \end{array}$$ calculate \(\Delta H\) for the reaction $$\mathrm{P}_{4} \mathrm{O}_{10}(s)+6 \mathrm{PCl}_{5}(g) \longrightarrow 10 \mathrm{Cl}_{3} \mathrm{PO}(g)$$

Why is it a good idea to rinse your thermos bottle with hot water before filling it with hot coffee?
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